arXiv:2512.19978quant-phcs.AI2025-12

用遗传算法自动设计紧凑量子神经网络,实现高效函数回归。

Regression of Functions by Quantum Neural Networks Circuits

  • 基于遗传算法优化电路深度、参数门配置和数据重加载模式。
  • 在22个非线性函数上表现媲美经典模型,参数量远少于后者。
  • 复杂度指标可精准预测最佳量子架构,适合自动化模型选择。

量子神经网络性能高度依赖于架构设计,包括电路深度、参数门位置及数据编码策略。本文研究回归任务的自动化量子电路构建,提出一种遗传算法框架,用于发现简化型量子回归器(Reduced Regressor QNN)架构。该方法探索电路深度、参数门配置与灵活的数据重加载模式,将量子回归器构造视为优化问题。所发现的电路在22个非线性基准函数和4个解析函数上,与17种经典回归模型对比,虽经典方法常达相当精度,但通常需更多参数,而演化出的量子模型保持紧凑且性能竞争。进一步通过12种结构描述符分析数据集复杂度,在五个逐步增强的元学习场景中,这些度量能可靠预测最优量子架构,部分场景下预测准确率达完美或近完美。结果表明,复杂度指标为数据集结构提供了强大而紧凑的表征,可有效指导自动化模型选择。本研究为元学习驱动的量子架构设计提供理论基础,深化了对量子模型在回归任务中行为的理解,填补了此前研究空白,推动量子回归走向系统化与理论化。

原文摘要 · Abstract (English)

The performance of quantum neural network models depends strongly on architectural decisions, including circuit depth, placement of parametrized operations, and data-encoding strategies. Selecting an effective architecture is challenging and closely related to the classical difficulty of choosing suitable neural-network topologies, which is computationally hard. This work investigates automated quantum-circuit construction for regression tasks and introduces a genetic-algorithm framework that discovers Reduced Regressor QNN architectures. The approach explores depth, parametrized gate configurations, and flexible data re-uploading patterns, formulating the construction of quantum regressors as an optimization process. The discovered circuits are evaluated against seventeen classical regression models on twenty-two nonlinear benchmark functions and four analytical functions. Although classical methods often achieve comparable results, they typically require far more parameters, whereas the evolved quantum models remain compact while providing competitive performance. We further analyze dataset complexity using twelve structural descriptors and show, across five increasingly challenging meta-learning scenarios, that these measures can reliably predict which quantum architecture will perform best. The results demonstrate perfect or near-perfect predictive accuracy in several scenarios, indicating that complexity metrics offer powerful and compact representations of dataset structure and can effectively guide automated model selection. Overall, this study provides a principled basis for meta-learning-driven quantum architecture design and advances the understanding of how quantum models behave in regression settings--a topic that has received limited exploration in prior work. These findings pave the way for more systematic and theoretically grounded approaches to quantum regression.

量子神经网络函数回归自动化设计

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